Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences)

A readable, straightforward guide by two authors with extensive experience in the field. This text shows how to recognize NP-complete problems and offers practical suggestions for dealing with them effectively. It is suitable as a supplement to courses in algorithm design, computational complexity, operations research, or combinatorial mathematics, and as a text for seminars on approximation algorithms or computational complexity.

This book's introduction features a humorous story of a man with a line of people behind him, who explains to his boss, "I can't find an efficient algorithm, but neither can all these famous people." This man illustrates an important quality of a class of problems, namely, the NP-complete problems: if you can prove that a problem is in this class, then it has no known polynomial-time solution that is guaranteed to work in general. This quality implies that the problem is difficult to deal with in practice.

The focus of this book is to teach the reader how to identify, deal with, and understand the essence of NP-complete problems; Computers and Intractability does all of those things effectively. In a readable yet mathematically rigorous manner, the book covers topics such as how to prove that a given problem is NP-complete and how to cope with NP-complete problems. (There is even a chapter on advanced topics, with numerous references.) Computers and Intractability also contains a list of more than 300 problems--most of which are known to be NP-complete--with comments and references.